Lyapunov Functional Method for 1D Radiative and Reactive Viscous Gas Dynamics

We consider the compressible Navier–Stokes system for 1D-flows of a viscous heat-conducting gas, with the pressure law Open image in new window and a one-order kinetics to include radiative effects and reactive processes. The mass force and the ignition phenomenon are also taken into account. For large data and under general assumptions on the heat conductivity, we establish global-in-time bounds and exponential stabilization for solutions in L q and H1 norms. To this end, we construct new global Lyapunov functionals and show that they describe the dynamics of solutions for any t≧0. A short proof of the corresponding global existence is also included for completeness.